Difference between revisions of "SIR Modeling"
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<center><math>S_{t+1} = S_t - \beta S_t I_t</math></center> | <center><math>S_{t+1} = S_t - \beta S_t I_t</math></center> | ||
+ | |||
+ | <center><math>I_{t+1} = I_t + \beta S_t I_t - \gamma I_t</math></center> | ||
+ | |||
+ | <center><math>R_{t+1} = R_t + \gamma I_t</math></center> | ||
where; | where; | ||
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<math>S</math> number of susceptible individuals, | <math>S</math> number of susceptible individuals, | ||
− | <math>I</math> number of infected individuals | + | <math>I</math> number of infected individuals, |
− | < | + | <math>R</math> number of recovered individuals, |
+ | |||
+ | <math>\beta</math> the average number of contacts per person per time, | ||
− | + | <math>\gamma</math> the transition rate. |
Compartmental Modeling
Discrete-time SIR modeling of infections/recovery
The model consists of individuals who are either Susceptible ([math]S[/math]), Infected ([math]I[/math]), or Recovered ([math]R[/math]).
The epidemic proceeds via a growth and decline process. This is the core model of infectious disease spread and has been in use in epidemiology for many years.
The dynamics are given by the following 3 equations.
where;
[math]S[/math] number of susceptible individuals,
[math]I[/math] number of infected individuals,
[math]R[/math] number of recovered individuals,
[math]\beta[/math] the average number of contacts per person per time,
[math]\gamma[/math] the transition rate.
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